Autoregressive model for time-series data

Abstract

A technique includes fitting an autoregressive integrated moving average (ARIMA) model to time-series data. The technique further includes the computation of autoregression coefficients from the ARIMA model applied to the time-series data. The autoregression coefficients may be usable for data classification purposes.

What is claimed is: 
     
         1 . A method, comprising:
 collecting time-series data;   fitting, by an autoregression model fit engine, an autoregressive integrated moving average (ARIMA) model to the time-series data to compute autoregression coefficients; and   classifying, by a classification engine, the time-series data based on the autoregression coefficients.   
     
     
         2 . The method of  claim 1  wherein classifying the time-series data comprises performing discriminative analysis. 
     
     
         3 . The method of  claim 1  wherein classifying the time-series data comprises performing linear or quadratic discriminative analysis. 
     
     
         4 . The method of  claim 1  wherein classifying the time-series data comprises performing template matching using orthogonal matching pursuit. 
     
     
         5 . The method of  claim 1  further comprising computing cepstrum coefficients from the autoregression coefficients. 
     
     
         6 . The method of  claim 5  wherein classifying the time-series data comprises:
 selecting a basis vector that has a largest correlation to the cepstrum coefficients; 
 computing the residual of the time-series data using the selected basis vector; and 
 computing the L2 norm of the residual. 
 
     
     
         7 . The method of  claim 1  further comprising, for each of a plurality of training data sets, each training data set corresponding to one of a plurality of classifications, fitting an ARIMA model to the training data set to compute autoregression coefficients, and wherein classifying the time-series data comprises using both the autoregression coefficients and the autoregression training coefficients. 
     
     
         8 . The method of  claim 1  further comprising converting the autoregression coefficients to cepstrum coefficients and wherein classifying the time-series data uses the cepstrum coefficients. 
     
     
         9 . The method of  claim 1  further comprising removing a linear trend from the time-series data. 
     
     
         10 . A non-transitory, computer-readable storage device containing software that, when executed by a processor, causes the processor to:
 fit an autoregressive model to time-series data to compute autoregression coefficients;   convert the autoregression coefficients to cepstrum coefficients; and   classify the time-series data based on the cepstrum coefficients.   
     
     
         11 . The non-transitory, computer-readable storage device of  claim 10  wherein the software causes the processor to classify the time-series data by performing at least on one of linear discriminative analysis, quadratic discriminative analysis, and template matching using orthogonal matching pursuit. 
     
     
         12 . The non-transitory, computer-readable storage device of  claim 10  wherein the software causes the processor to fit to the time series-data an autoregression model that is based on either Yule-Walker equations or a Levinson-Durbin iterative procedure. 
     
     
         13 . The non-transitory, computer-readable storage device of  claim 10  wherein the software causes the processor to compute autoregression coefficients for each of a plurality of training data sets, each training data corresponding to one of a plurality of classifications. 
     
     
         14 . The non-transitory, computer-readable storage device of  claim 11  wherein the software causes the processor to classify the time-series data based on the cepstrum coefficients and the autoregression coefficients for each of the plurality of classifications. 
     
     
         15 . The non-transitory, computer-readable storage device of  claim 11  wherein the software causes the processor to convert the autoregression coefficients for each of the plurality of classifications into cepstrum coefficients for each of the plurality of classifications and to classify the time-series data based on both the cepstrum coefficients from the time-series data and from each of the plurality of classifications. 
     
     
         16 . The non-transitory, computer-readable storage device of  claim 11  wherein the software causes the processor to classify the time-series data by:
 selecting a basis vector that has a largest correlation to the cepstrum coefficients; 
 computing the residual of the time-series data using the selected basis vector; 
 computing the L2 norm of the residual; 
 computing an error for each of a plurality of regimes until the L2 norm is less than a threshold; and 
 selecting a regime for classification resulting in the smallest error. 
 
     
     
         17 . A system, comprising:
 an autoregressive integrated moving average (ARIMA) model fit engine to receive time-series training data for each of a plurality of regimes and to fit an ARIMA model to the time-series training data to thereby generate autoregression coefficients; and   a cepstrum coefficient engine to generate cepstrum coefficients based on the autoregression coefficients, the cepstrum coefficients usable to classify live time-series data into one of the regimes.   
     
     
         18 . The system of  claim 17  wherein the ARIMA model fit engine is to remove a linear trend from the time-series training data to produce residuals. 
     
     
         19 . The system of  claim 17  wherein the cepstrum coefficient engine is to generate the cepstrum coefficients for each of a plurality of frames of time-series training data of each regime and to average a subset of the cepstrum coefficients across the frames. 
     
     
         20 . The system of  claim 17  further comprising a classification engine to classify live time-series data based on the cepstrum coefficients.